## 1B.15

Chris Tai 1B
Posts: 102
Joined: Sat Aug 24, 2019 12:16 am

### 1B.15

The velocity of an electron that is emitted from a metallic surface by a photon is 3.6x10^3 km/s. (a) What is the wavelength of the ejected electron? (b) No electrons are
emitted from the surface of the metal until the frequency of the radiation reaches 2.50 3 1016 Hz. How much energy is required to remove the electron from the metal surface? (c) What is the wavelength of the radiation that caused photoejection of the electron? (d) What kind of electromagnetic radiation was used?

How would I complete part a / how is the kinetic energy of the ejected electron related to the wavelength of that electron? I know that (wavelength)(frequency) = 3x10^8 but I'm entirely sure if that applies to electrons as well.

Chem_Mod
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Joined: Thu Aug 04, 2011 1:53 pm
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### Re: 1B.15

You would use E=hv=1/2mv2 + threshold energy.
And then from there you could plug it into c=wavelength x frequency.
Hope this helps :)

JasonLiu_2J
Posts: 109
Joined: Sat Aug 24, 2019 12:17 am

### Re: 1B.15

Just to add on, to find the wavelength of the ejected electron, you can also use the De Broglie equation, which provides a relationship between wavelength and momentum. The De Broglie equation indicates that the wavelength is equal to Planck's constant divided by the momentum of the object in question (λ=h/p). Remember that momentum is equal to mass x velocity, or p=mv, which means that you can state the De Broglie equation as λ=h/(mv). You are given the velocity of the ejected electron and you know that the mass of one electron is 9.11 x 10^-31 kg (given in the list of constants). Before you substitute the values into the equation, you need to check for the units. Mass should be in kilograms and velocity should be in meters/second. Mass is in the right units, but the velocity is given in kilometers/second. Converting this to m/s, you will get 3.6 x 10^6 m/s as your velocity. Finally, if you plug the mass and velocity into the De Broglie equation, you will find be able to calculate the wavelength, which turns out to be about 2.02 x 10^-10 m, or 202 pm. Essentially, you can relate the velocity of the electron to the wavelength of the electron using the De Broglie equation. Hope this helps!